**Memoirs of the American Mathematical Society**

2009;
102 pp;
Softcover

MSC: Primary 20;

Print ISBN: 978-0-8218-4462-5

Product Code: MEMO/202/947

List Price: $70.00

Individual Member Price: $42.00

**Electronic ISBN: 978-1-4704-0561-8
Product Code: MEMO/202/947.E**

List Price: $70.00

Individual Member Price: $42.00

# Rock Blocks

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*W. Turner*

Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to \(q\)-Schur algebras, or to finite general linear groups in non-describing characteristic. Rock blocks are certain combinatorially defined blocks appearing in such a representation theory, first observed by R. Rouquier. Rock blocks are much more symmetric than general blocks, and every block is derived equivalent to a Rock block. Motivated by a theorem of J. Chuang and R. Kessar in the case of symmetric group blocks of abelian defect, the author pursues a structure theorem for these blocks.

#### Table of Contents

# Table of Contents

## Rock Blocks

- Introduction 110 free
- Chapter 1. Highest weight categories, 𝑞-Schur algebras, Hecke algebras, and finite general linear groups 716 free
- Chapter 2. Blocks of 𝑞-Schur algebras, Hecke algebras, and finite general linear groups 1928
- Chapter 3. Rock blocks of finite general linear groups and Hecke algebras, when 𝑤<𝑙 2736
- Chapter 4. Rock blocks of symmetric groups, and the Brauer morphism 3342
- Chapter 5. Schur-Weyl duality inside Rock blocks of symmetric groups 3948
- Chapter 6. Ringel duality inside Rock blocks of symmetric groups 4958
- Chapter 7. James adjustment algebras for Rock blocks of symmetric groups 5766
- Chapter 8. Doubles, Schur super-bialgebras, and Rock blocks of Hecke algebras 6776
- Chapter 9. Power sums 8594
- Chapter 10. Schiver doubles of type 𝐴_{∞} 91100
- Bibliography 97106